# Maths

posted by .

A straight river flows at a speed of 20km/h. A boater starts at the south shore and heads in ths direction of 70degrees from the shore. The boat has a speed of 20km/h in still water. Find the true speed and direction of the boat.

• Maths -

Let the river flow in the +x direction.
Across the river is then +y.

river velocity = (20,0)
boat velocity relative to the water
= (20cos70°,20sin70°) = (6.84,18.79)

resultant velocity relative to land
= (26.84,18.79)

speed: √(26.8^2+18.79^2) = 32.73
direction:
tanθ = y/x = 18.79/26.84 = .70
θ = 35°

## Similar Questions

1. ### Math: Calculus - Vectors

A boat travels at a speed of 5 m/s in still water. The boat moves directly across a river that is 70m wide. The water in the river flows at a speed of 2 m/s. How long does it take the boat to cross the river?
2. ### Physics

A motorboat heads due east at 8.5 m/s across a river that flows to the south at a speed of 2.5 m/s. a. What is the velocity of the boat relative to a stationary observer on the shore?
3. ### Physics

A river is flowing 4.0 m/s to the east. A boater on the south shore plans to reach a dock on the north shore 30.0 Degrees downriver by heading directly across the river. What should be the boat's speed relative to the water?
4. ### Physics

A river is flowing 4.0 m/s to the east. A boater on the south shore plans to reach a dock on the north shore 30.0 Degrees downriver by heading directly across the river. What should be the boat's speed relative to the water?
5. ### physics

A river flows due east at 1.50 m/s. A boat crosses the river from the south shore to the north shore by maintaining a constant velocity of 9.2 m/s due north relative to the water. (a) What is the velocity of the boat as viewed by an …
6. ### Physics

A boat crosses a river of width 113 m in which the current has a uniform speed of 0.933 m/s. The pilot maintains a bearing (i.e., the direction in which the boat points) perpendicular to the river and a throttle setting to give a constant …
7. ### Pre calculus, vectors

A straight river flows at a speed of 20km/h. A boater starts at the south shore and heads in ths direction of 70degrees from the shore. The boat has a speed of 20km/h in still water. Find the true speed and direction of the boat.
8. ### physics

a river flows due east at 1.50 m/s. A boat crosses the river from the south shore to the north shore by maintaining a constant velocity of 10m/s due north relative to the water. (a) what is the velocity of the boat relative to the …
9. ### Physics

a boat crosses a 2 km wide river by starting out at the south shore and heading directly for the north shore if the river flows at 0.8 m/s and the boat can go at 1.4 m/s in still water, where on the opposite shore will the boat land?
10. ### Physics

a boat crosses a 2 km wide river by starting out at the south shore and heading directly for the north shore if the river flows at 0.8 m/s and the boat can go at 1.4 m/s in still water, where on the opposite shore will the boat land?

More Similar Questions